Towards More Reasonable Evolution by Eckard Blumschein

Eckard,

you made a comment to George Simpson that perhaps should have been addressed to Gary Simpson. (I'm sure George would have been completely mystified!)

Hi Eckard,

I just read your nice essay. Like you I see Ockham's razor a very useful tool to decide what is true in physics.

I hope you do well in the competition.

Regards,

Akinbo

Dear Eckard Blumschein,

Great said about the static monism of Einstein and that he had a problem with the sense of reality.

It is necessary to distinguish geometrical space from physical space. It is a different concept. Geometric space does not move, and the physical space is in constant movement, forming the whole world

I inform all the participants that use the online translator, therefore, my essay is written badly. I participate in the contest to familiarize English-speaking scientists with New Cartesian Physic, the basis of which the principle of identity of space and matter. Combining space and matter into a single essence, the New Cartesian Physic is able to integrate modern physics into a single theory.

Don't let the New Cartesian Physic disappear! Do not ask for himself, but for Descartes.

New Cartesian Physic has great potential in understanding the world. To show potential in this essay I risked give "The way of The materialist explanation of the paranormal and the supernatural" - Is the name of my essay.

Visit my essay and you will find something in it about New Cartesian Physic. After you give a post in my topic, I shall do the same in your theme. I wish not to interrupt our communication

Sincerely,

Dizhechko Boris

Eckard,

I agree that: "World's population must be stabilized without naturally correcting catastrophes like decimating wars or mass starvation." There is not enough discussion of this important issue so I'm really glad that you mentioned it in your essay.

However, without genuine free will, ethical goals are useless. If human beings are not able to freely move relative to the "block universe" to navigate towards an imagined ethical goal, then what will be will be. Que sera sera.

Regards,

Lorraine

Eckard, I'm glad you enjoyed reading the thread on Dedekind's axiom: the style of Canute is excellent. I think many here in FQXi forums and contests could learn something from him (including myself, of course).

I just downloaded Prof. Mückenheim's sourcebook. It seems very rich and interesting, certainly very useful for me, regardless of whether or not I agree with the conclusions.

You say: "I see Dedekind and G. Cantor having established the impossible: a continuous line that is composed of distinguishable from each other points."

It seems to me that your words express, referring to the linear order of the real numbers, the meaning of the axiom of choice. Gödel and Cohen demonstrated its independence from the other axioms of Zermelo and Fraenkel. Many mathematicians accept it (more or less implicitly). Others prefer to do without it (usually explicitly). It may be that it is an expression of our defective or erroneous way to consider the real numbers. But it may be that it reflects some deep aspect of their reality and of the nature of mathematical infinity, an infinity that we are not able to completely grasp.

I agree with you that perhaps we will never know if space and time are finite or infinite. In fact we don't know, after 2500 years of theory and research, what they are. And we don't even know what the numbers are, if they are discovered or invented, if they exist outside the mind or are just a product of it, if they are dicrete or continuous, if they are in a sort of Plato's hyperuranium or of Cantor's "paradise" (or Cantor seen by Hilbert's eyes).

I don't think that all sets of numbers we know and use are mental constructs. So are many of them, like the infinite hierarchy of Cantor's transfinite, and probably also imaginary numbers. I tend to think, however, that there is a link between the natural numbers, the positive real numbers, and the world. I find it hard to think, for example, that Pi is only the result of mind's creativity.

In the 2015 contest, I have proposed the hypothesis that real numbers (suitably ordered), space, and time are the same thing, at least for all the reference frames that travel at speeds below that of light. I am not able to prove this hypothesis, nor to deal on my own with all the complexity of the issues it raises. But I think I can argue (as I did in a book and partially in the current contest), it allows to capture som aspects of the nature of time (as long as we exclude the axiom of choice) and probably to explain the possibility of motion and change, very common phenomena that have been always a source of difficulties and paradoxes.

I think I have dwelt too much in this post. But I think also it is a pleasure to converse with you, Eckard.

Best regards again,

Giovanni

Daer Giovanni,

A canoe is a small narow boat. Canoeing is a sport. Canute is a German word. Maybe, Ute Can is a female German.

Concerning the axiom of choice I will quickly translate what Mückenheim wrote in his "Die Geschichte des Unendlichen", Augsburg 2004:

"At a meeting of German society of mathematicians in 1904, the Hungarian mathematician Julius König presented his proof that the real numbers cannot be well-ordered. A counter example would be the best and most convincing method to refute this claim. However, nobody was able to constuct it because König was de facto correct. So far, everybody failed to well-order the real numbers, and there is no serious mathematician who believes in the possibility of success.

Nonetheless, König's proof has today been considered wrong: The controversy made Cantor upset who felt his life work endangered. Immediately after it, Ernst Zermelo (1871-1953) fabricated the axiom of choice."

You wrote:

"But it may be that [AC] reflects some deep aspect of their reality and of the nature of mathematical infinity, an infinity that we are not able to completely grasp."

In contrast to the logical notion of infinite, the mathematical infinity is merely a pragmatic creation by Leibniz and Bernoulli. It can be used as if it was really strictly logically founded. However, it was certainly not by chance that Cauchy begun lecturing a class of 30 students and lost all but one.

You wrote:

"I find it hard to think, for example, that Pi is only the result of mind's creativity."

Well, consequent thinking is rare. Mückenheim denies the actual infinity. Consequently he should also deny the real number zero, and in a next step any real number. Mathematics claims all real numbers to be as distinguishable as definitely are the integer and rational ones. From the perspective of a continuum every part of which has parts, and a point being something that doesn't have parts, I see the mandatory notion of real numbers a self-deception. Strictly speaking, continuum and numbers exclude and complement each other.

Best regards,

Eckard